Determine x so that x, 1/2x+7, and 3x-1 are the first three terms of an arithmethic sequence?

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Answer 1 · 2018-07-01T20:59:56

Common difference between the terms must be equal, therefore

$t_2 -t_1 = t_3 - t_2$

$1/2x +7 -x = 3x-1-(1/2x +7)$

$-1/2x + 7 = 3x - 1 - 1/2x - 7$

$15 =3x$

$x=5$

We can confirm by plugging in $5$ for $x$ to see that the terms of the sequence are $5, 19/2, 14$ which do indeed for an arithmetic sequence.

Hopefully this helps!